The British government's brand new counter-terrorism strategy is already in disarray - and ministers have only themselves to blame. The souped-up plan to fight al-Qaida, confound dirty bombers, halt suicide attacks and confront "extremism" in the country's Muslim community was unveiled by the prime minister with much fanfare on Tuesday. But even before the 175-page "Contest 2" document had been launched, the credibility of its promise to engage with the Muslim mainstream had been thrown into question by the decision of Hazel Blears, the communities secretary, to cut all links with the Muslim Council of Britain.

Blears had been gunning for the MCB, the country's main Muslim umbrella body, which has shown increasing independence in recent years, particularly in relation to British foreign policy. The pretext was a statement about Israel's onslaught on Gaza signed by the MCB's number two, Daud Abdullah, which Blears interpreted as a call for attacks on British ships if they were sent to intercept arms supplies to Hamas. Ten days ago, in a tone more associated with Raj-era colonial governors than democratic politicians addressing independent community bodies, Blears delivered an ultimatum to the MCB: either it sacked its elected deputy general secretary or all contacts would be severed.

Never mind that Gordon Brown's idea about policing Palestinian waters has been kicked into the long grass of international talks; or that Abdullah, a Caribbean-born veteran of Grenada's leftwing New Jewel Movement (later overthrown by Ronald Reagan) made clear he was not calling for such attacks - let alone attacks on Jewish communities, as Blears claims in a letter in today's Guardian. All links have now been suspended. And if there were any doubt that the attempt to isolate Britain's most significant Muslim body was linked to the new anti-terror policy, the timing of the ultimatum for the eve of the launch made clear that for Blears they were all of a piece.

Not surprisingly, the MCB has rejected the government's diktat. As it acknowledges, to do anything else would destroy its credibility in the community, which can in fact only be boosted by the confrontation. The point seems to have belatedly dawned on Blears, whose department yesterday appeared to be looking for a way out as it pressed for "further clarity" from the MCB about its attitude to violence in the Middle East.

But the dispute goes to the heart of the fatal flaw in government policy towards the terror threat. Instead of simply aiming to stop indiscriminate attacks, something that unites almost all Muslims as well as non-Muslims, the idea underlying the new strategy is to confront "nonviolent extremism" as well. The definitions of such a catch-all target specified in earlier drafts, including support for armed resistance anywhere in the world, sharia law and a belief that gay sex is sinful, have mercifully been dropped. It became clear to other ministers - reported to include Jack Straw, John Denham and Harriet Harman - that not only would such zealotry brand most of Britain's 2.4 million Muslims extremist, it could also apply to many Christians, orthodox Jews and atheists as well.

But strong echoes of this folly remain: for example, in the categorisation of those who reject Israel's legitimacy as extremist. It is a policy that has been driven by neoconservative-leaning thinktanks - such as Policy Exchange, the Centre for Social Cohesion and the government-funded Quilliam Foundation - who believe Islamism, a political trend as broad as socialism or liberalism, is the enemy, rather than the tiny takfiri groups who think it's a good idea to blow people up on buses and tubes.

That's a dangerous blind alley, which makes such attacks more, rather than less, likely. Instead of listening to representative groups which can honestly reflect what drives Muslim anger - notably western support for wars of occupation in the Muslim world - the government ends up talking to its own creations and attempting to use cash to buy political docility. It is the same approach which preferred listening to republican defectors than Sinn Féin in Northern Ireland, as the former chief of the defence staff Lord Guthrie enthusiastically emphasised this week.

The Contest 2 strategy has one merit, at least. It does for the first time officially acknowledge what the rest of the world has known for most of the past decade: that Muslim "perception" of the west's support for Israel, the Iraq and Afghan wars and the wider war on terror plays a "key role" in fuelling "radicalisation". But instead of then getting to grips with the cause of the problem, the response is still to treat the symptoms. Since Israel's western-backed devastation of Gaza unleashed a new wave of Muslim political activism, for example, the reaction has been heavyhanded policing, attempts to link protest with terrorism and renewed Islamophobic campaigns in the media.

Perhaps Blears thought attacking the MCB would play to the gallery in such a climate. But as the Jewish Chronicle columnist Geoffrey Alderman warned yesterday, not only was her interference a democratic outrage, but a dangerous precedent for other community organisations. Would Blears refuse to engage with a Jewish Board of Deputies leader, he asked, who backed West Bank settlements the government regards as illegal? Muslims are already angered by the double standards that allow Britons to serve with Israeli forces in Gaza and the Zionist Federation to raise charitable funds for occupation troops accused of war crimes, while any parallel moves to support Hamas are treated as involvement in terrorism.

The government preaches globalisation but has failed to face up to the implications of the multiple identities and loyalties that flow from it. The presence of a large population with recent roots in a part of the world where British forces are fighting unpopular wars is one reason why domestic and foreign policy can never again be separated in the way that was possible in colonial times. The government's counter-terrorism plan talks about Muslims needing to accept Britain's shared values. Fortunately, they do already. Both Muslims and non-Muslims oppose wars of aggression and want British troops brought home from Iraq and Afghanistan; they both accept people's right to defend themselves against invasion and occupation; and both mostly sympathise with the Palestinian cause. Now responding to that consensus would be a real counter-terror strategy.

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